Dual solutions for Casson hybrid nanofluid flow due to a stretching/shrinking sheet: A new combination of theoretical and experimental models

Mousavi, Seyed Mahdi; Rostami, Mohammadreza Nademi; Yousefi, Mohammad; Dinarvand, Saeed; Pop, Ioan; Sheremet, Mikhail А.

doi:10.1016/j.cjph.2021.04.004

Cited by 82 publications

(36 citation statements)

References 29 publications

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“…These findings align with the results presented in Figure 4 and Figure 10 (for certain values of  and A ) and Figure 5 and Figure 11 (for all values of  and A considered), respectively. As can be seen from these figures, the boundary layer thickness for the first solution is smaller than the second solution as reported by many researchers such as Aladdin et al, [43] and Mousavi et al, [54]. Since dual solutions are obtained in this study, the stability analysis is performed to determine the stability of solutions by finding the smallest eigen value  .…”

Section:  mentioning

confidence: 60%

Stability Solution of Unsteady Stagnation-Point Flow and Heat Transfer over a Stretching/Shrinking Sheet in Nanofluid with Slip Velocity Effect

Dzulkifli

Bachok

Yacob

et al. 2022

CFDL

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Computational of unsteady flow with slip condition is essential since physically the heat transfer process is time-dependent and there may exist slip between fluid and surface. Therefore, this study aims to investigate the unsteady stagnation-point flow and heat transfer over a stretching/shrinking sheet immersed in nanofluid in the presence of slip velocity. By applying boundary layer theory and Tiwari-Das model, the governing equations are developed and transformed into a system of ordinary differential equations using similarity transformation, which are then solved numerically using bvp4c solver in MATLAB. The influence of slip velocity, stretching/shrinking parameters, nanoparticle volume fraction and unsteadiness parameter on the local skin friction coefficient, local Nusselt number, as well as velocity and temperature profiles are analysed. There are three types of nanoparticles considered, namely Copper (Cu), Alumina (Al203), Titania (TiO2) and water (H20) is the base fluid. It is found that dual solutions occur for certain parameters and the stability analysis is performed. The analysis shows that the first solutions are found to be stable than the second solution. The local skin friction coefficient and local Nusselt number are increasing with slip velocity, nanoparticle volume fraction for shrinking case; however, the opposite trend is observed for stretching case. By raising 20% of nanoparticle volume fraction for the shrinking sheet ( the friction at the surface increases 24% and 15.5% for heat transfer rate for the first solution. Moreover, for 10% of nanoparticle volume fraction for the shrinking sheet (and the first solution, varying slip parameters from 0 to 0.2, give rise to approximately 21% of the friction at the surface and 68% of the heat transfer rate.

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Section:  mentioning

confidence: 60%

Stability Solution of Unsteady Stagnation-Point Flow and Heat Transfer over a Stretching/Shrinking Sheet in Nanofluid with Slip Velocity Effect

Dzulkifli

Bachok

Yacob

et al. 2022

CFDL

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“…With the above assumptions, the mathematical model takes the form 57 :

{\overset{true¯}{u}}_{x} + {\overset{true¯}{v}}_{y} + {\overset{true¯}{w}}_{z} = 0,

\overset{u}{true} {\overset{true¯}{u}}_{x} + \overset{v}{true} {\overset{true¯}{u}}_{y} + \overset{w}{true} {\overset{true¯}{u}}_{z} = ν_{h n f} (1 + \frac{1}{β}) {\overset{true¯}{u}}_{z z} - \frac{σ_{h n f}}{ρ_{h n f}} B^{2} \overset{u}{true},

\overset{u}{true} {\overset{true¯}{v}}_{x} + \overset{v}{true} {\overset{true¯}{v}}_{y} + \overset{w}{true} {\overset{true¯}{v}}_{z} = ν_{h n f} (1 + \frac{1}{β}) {\overset{true¯}{v}}_{z z} - \frac{σ_{h n f}}{ρ_{h n f}} B^{2} \overset{v}{true},

\overset{u}{true} {\overset{true¯}{T}}_{x} + \overset{v}{true} {\overset{true¯}{T}}_{x} + \overset{w}{true} {\overset{true¯}{T}}_{z} = \frac{κ_{h n f}}{{(ρ C_{p})}_{h n f}} {\overset{true¯}{T}}_{z z} .

…”

Section: Mathematical Modelmentioning

confidence: 99%

The analogy of nanoparticle shapes on the theory of convective heat transfer of Au–Fe₃O₄ Casson hybrid nanofluid

2021

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In recent times, Au nanoparticles have been commonly used for delivering the drug especially in the case of hypothermia of tumors, but low absorption of IR light does not solve destruction of tumor cells. However, nanoparticles such as Fe3O4 coated with Au could be used to deliver the drug to a specific spot due to applied external magnetic field. Due to these applications, boundary layer approximation is invoked to simplify the mathematical model. This paper presents the nanoparticle shape analysis and heat transfer features of the Au–Fe3O4–blood hybrid nanofluid flowing past a stretching surface on a magnetohydrodynamic medium. Numerical solutions of nonlinear differential equations are obtained by RKF‐45 method with the help of shooting technique. The behavior of emerging parameters is described graphically for velocity and temperature profiles. It is found that the blade‐shaped Au and Fe3O4 nanoparticles have better thermal conductance than brick, sphere, cylinder, needle, and platelet shapes. It is also observed that the Lorentz force generated due to magnetic field helps in controlling the flow and enhance the thermal conductivity of hybrid nanofluid.

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“…Dinarvand et al 31 discussed improvement in micro-circulatory process inserting role of hybrid nano-structures over a porous surface. Mousavi et al 32 investigated performance of Casson liquid and dual solutions of developed model using nanoparticles over an expanding surface. Dinarvand et al 33 analyzed swirling flow in mass-based model using hybrid nanoparticles via von Kármán’s theory.…”

Section: Introductionmentioning

confidence: 99%

Investigation of thermal performance of Maxwell hybrid nanofluid boundary value problem in vertical porous surface via finite element approach

Algehyne

El‐Zahar

Elhag

et al. 2022

Sci Rep

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The study of thermo-physical characteristics is essential to observe the impact of several influential parameters on temperature and velocity fields. The transportation of heat in fluid flows and thermal instability/stability is a charming area of research due to their wider applications and physical significance because of their utilization in different engineering systems. This report is prepared to study thermal transportation in Maxwell hybrid nanofluid past over an infinite stretchable vertical porous sheet. An inclusion of hybrid nanofluid is performed to monitor the aspects of thermal transportation. Keeping in mind the advantages of thermal failure, non-Fourier theory for heat flux model is utilized. Aspects of external heat source are also considered. The mathematical formulation for the considered model with certain important physical aspects results in the form of coupled nonlinear PDEs system. The obtained system is reduced by engaging boundary layer approximation. Afterwards, transformations have been utilized to convert the modeled PDEs system into ODEs system. The converted nonlinear ODEs system is then handled via finite element method coded in symbolic computational package MAPLE 18.0. Grid independent survey is presented for the validation of used approach and the comparative analysis has been done to confirm the reliability of obtained solution. The obtained solution is discussed and physical aspects have been explored and recorded against numerous involved influential variables. Motion into hybrid nanoparticles and nanoparticles becomes slow down versus higher values of Forchheimer and Darcy’s porous numbers. Thermal growth is enhanced for the case of hybrid nano-structures rather than for case of nanofluid. Thickness regarding momentum layer is dominated for hybrid nanoparticles rather than case of nanoparticles.

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Dual solutions for Casson hybrid nanofluid flow due to a stretching/shrinking sheet: A new combination of theoretical and experimental models

Cited by 82 publications

References 29 publications

Stability Solution of Unsteady Stagnation-Point Flow and Heat Transfer over a Stretching/Shrinking Sheet in Nanofluid with Slip Velocity Effect

Stability Solution of Unsteady Stagnation-Point Flow and Heat Transfer over a Stretching/Shrinking Sheet in Nanofluid with Slip Velocity Effect

The analogy of nanoparticle shapes on the theory of convective heat transfer of Au–Fe₃O₄ Casson hybrid nanofluid

Investigation of thermal performance of Maxwell hybrid nanofluid boundary value problem in vertical porous surface via finite element approach

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Dual solutions for Casson hybrid nanofluid flow due to a stretching/shrinking sheet: A new combination of theoretical and experimental models

Cited by 82 publications

References 29 publications

Stability Solution of Unsteady Stagnation-Point Flow and Heat Transfer over a Stretching/Shrinking Sheet in Nanofluid with Slip Velocity Effect

Stability Solution of Unsteady Stagnation-Point Flow and Heat Transfer over a Stretching/Shrinking Sheet in Nanofluid with Slip Velocity Effect

The analogy of nanoparticle shapes on the theory of convective heat transfer of Au–Fe3O4 Casson hybrid nanofluid

Investigation of thermal performance of Maxwell hybrid nanofluid boundary value problem in vertical porous surface via finite element approach

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The analogy of nanoparticle shapes on the theory of convective heat transfer of Au–Fe₃O₄ Casson hybrid nanofluid